5(2x+3)=2x(3x+1)

Solution for 5(2x+3)=2x(3x+1) equation:

5(2x+3)=2x(3x+1)

We move all terms to the left:

5(2x+3)-(2x(3x+1))=0

We multiply parentheses

10x-(2x(3x+1))+15=0


We calculate terms in parentheses: -(2x(3x+1)), so:

2x(3x+1)

We multiply parentheses

6x^2+2x

Back to the equation:

-(6x^2+2x)


We get rid of parentheses

-6x^2+10x-2x+15=0

We add all the numbers together, and all the variables

-6x^2+8x+15=0

a = -6; b = 8; c = +15;
Δ = b2-4ac
Δ = 82-4·(-6)·15
Δ = 424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{106}}{2*-6}=\frac{-8-2\sqrt{106}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{106}}{2*-6}=\frac{-8+2\sqrt{106}}{-12}
$